Én is oda megyek.

That’s right: Hungarian usually does not need the subject pronoun, because the verb ending already tells you who the subject is.

• megyek = I go / I’m going

So the sentence could simply be:

• Oda megyek.

Adding én makes the subject more explicit and often adds emphasis or contrast.

• Én is oda megyek. = I’m going there too / I also am going there

Here, én helps highlight I, especially together with is.

is usually means too, also, or sometimes even, depending on context.

In this sentence:

• én is = I too / I also

So is is showing that the speaker is being added to a group of people who are going there.

A very important point: is comes after the word it belongs to.

• én is = I too
• oda is = there too
• Péter is = Peter too

So in Én is oda megyek, the also applies specifically to I.

Because in Hungarian, is is a postposed particle: it normally comes after the word it modifies.

English says:

• I too
• I also

Hungarian says:

• én is

This is completely normal Hungarian structure. You will see the same pattern in many sentences:

• Anna is jön. = Anna is coming too.
• Ma is dolgozom. = I’m working today too.

oda is a directional adverb. It means something like:

• to there
• over there
• there in the sense of movement toward a place

So it is not just a general there. It implies going to that place.

A useful comparison:

• ott = there at a place, no movement
• oda = to there, movement toward that place

For example:

• Ott vagyok. = I am there.
• Oda megyek. = I’m going there.

megyek is the 1st person singular present tense form of menni (to go).

So:

• menni = to go
• megyek = I go / I’m going

A few present-tense forms are:

• megyek = I go
• mész = you go
• megy = he/she goes
• megyünk = we go
• mentek = you plural go
• mennek = they go

So the ending -ek here helps show that the subject is I.

In Hungarian, words like oda often act as a verbal modifier. In a neutral, affirmative sentence, that modifier usually stands directly before the verb.

So the natural neutral order is:

• oda megyek

This is very common in Hungarian:

• hazamegyek / haza megyek = I go home
• bemegyek = I go in
• felmegyek = I go up

If the sentence is negated or another element is strongly emphasized, the modifier often moves away from that position:

• Nem megyek oda. = I’m not going there.

So oda megyek is the normal basic order here.

No. Hungarian word order is flexible, but different orders often change the emphasis or information structure.

The most neutral version here is:

• Én is oda megyek.

But you may also hear things like:

• Oda megyek. = I’m going there.
• Én megyek oda. = I’m the one going there / I go there.
• Oda megyek én is. = I’m going there too.

These versions are not all interchangeable in tone. Hungarian word order often tells you what is being emphasized, not just who did what.

You can leave out én, but the meaning may become a little less explicit.

• Oda megyek. = I’m going there.

That still clearly means I, because megyek already shows 1st person singular.

However, if you want to say I too, then using én is is very natural:

• Én is oda megyek.

If the context already makes the subject obvious, Hungarian may also express the same idea in other ways, such as:

• Oda megyek én is.

So yes, én is optional grammatically, but useful when you want to stress I or say I too clearly.

It is formally present tense, but in Hungarian, the present tense can often refer to the near future, especially with motion verbs and when the context makes the time clear.

So Én is oda megyek can mean:

• I’m going there too
• I’ll go there too

The exact time depends on context.

For example:

• Most oda megyek. = I’m going there now.
• Holnap én is oda megyek. = Tomorrow I’ll go there too.

This is very normal in Hungarian.

A simple learner-friendly pronunciation is roughly:

• Én ≈ ayn
• is ≈ ish
• oda ≈ o-daw
• megyek ≈ MEH-dyek

A few useful notes:

• Hungarian stress is usually on the first syllable of each word.
• é is a long vowel.
• gy is a soft Hungarian consonant that does not exist exactly in English. A rough approximation is dy, but softer.

So the rhythm is roughly:

• ÉN is O-da MEH-dyek

Yes, but if you move is, you change what is being added.

Compare:

• Én is oda megyek. = I’m going there too.
• Én oda is megyek. = I go there too / I’m going there as well
  This suggests that there is one of several places.
• Péter is oda megy. = Peter is going there too.

So the position of is is very important. It follows the word that it emphasizes or includes in the also/too meaning.